Abstract
Percolation invasion displacement of a compressible defender is examined for two cases: when only the smallest accessible site is entered at each step and when all accessible sites less than the size given by a reducing back pressure are entered at each time step. Although the fractions of invading fluid are different, their scaling properties are equivalent. The effect of limited control of a back pressure in a real displacement and the effect of viscosity in a real time displacement are examined. In these cases the scaling properties of a percolation process at breakthrough are removed. As a result, one should expect that realistic displacement models will not have the singular properties usually attributed to percolation processes.
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Laidlaw, W.G., Hamilton, G.R., Flewwelling, R.B. et al. Fractal patterns of fluid domains for displacement processes in porous media. J Stat Phys 53, 713–731 (1988). https://doi.org/10.1007/BF01014222
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DOI: https://doi.org/10.1007/BF01014222